To simplify the expression [tex]\((x^m y^n)^2\)[/tex], we follow these steps:
1. Start with the given expression:
[tex]\[
(x^m y^n)^2
\][/tex]
2. Apply the power of a product property:
The power of a product property states that [tex]\((ab)^c = a^c \cdot b^c\)[/tex]. Here, we can apply this property to split the exponent:
[tex]\[
(x^m y^n)^2 = (x^m)^2 \cdot (y^n)^2
\][/tex]
3. Simplify each term:
- For the term [tex]\((x^m)^2\)[/tex], use the power of a power property which states that [tex]\((a^b)^c = a^{b \cdot c}\)[/tex]. Thus,
[tex]\[
(x^m)^2 = x^{m \cdot 2} = x^{2m}
\][/tex]
- Similarly, for the term [tex]\((y^n)^2\)[/tex], we have
[tex]\[
(y^n)^2 = y^{n \cdot 2} = y^{2n}
\][/tex]
4. Combine the simplified terms:
After simplifying both parts, we can combine them to get the final simplified expression:
[tex]\[
(x^m y^n)^2 = x^{2m} y^{2n}
\][/tex]
Thus, the simplified form of [tex]\((x^m y^n)^2\)[/tex] is:
[tex]\[
x^{2m} y^{2n}
\][/tex]
